Statistical Physics
Intuition tells us that an isolated physical system subjected to a sudden change (i.e., quenching) will evolve in a way that maximizes its entropy. If the system is in a pure, zero-entropy quantum state, it is expected to remain so even after quenching. How do we then reconcile statistical mechanics with quantum laws? To address this question, Kaufman et al. used their quantum microscope to study strings of six rubidium atoms confined in the wells of an optical lattice (see the Perspective by Polkovnikov and Sels). When tunneling along the strings was suddenly switched on, the strings as a whole remained in a pure state, but smaller subsets of two or three atoms conformed to a thermal distribution. The force driving the thermalization was quantum entanglement.
Science , this issue p. [794][1]; see also p. [752][2]
[1]: /lookup/doi/10.1126/science.aaf6725
[2]: /lookup/doi/10.1126/science.aah5776
Statistical Physics
Intuition tells us that an isolated physical system subjected to a sudden change (i.e., quenching) will evolve in a way that maximizes its entropy. If the system is in a pure, zero-entropy quantum state, it is expected to remain so even after quenching. How do we then reconcile statistical mechanics with quantum laws? To address this question, Kaufman et al. used their quantum microscope to study strings of six rubidium atoms confined in the wells of an optical lattice (see the Perspective by Polkovnikov and Sels). When tunneling along the strings was suddenly switched on, the strings as a whole remained in a pure state, but smaller subsets of two or three atoms conformed to a thermal distribution. The force driving the thermalization was quantum entanglement.
The dynamics and thermalization of classical systems have been extensively studied in the past. However, the corresponding quantum phenomena remain, to a large extent, uncharted territory. Recent experiments with ultracold quantum gases have at last allowed exploration of the coherent dynamics of isolated quantum systems, as well as observation of non-equilibrium phenomena that challenge our current understanding of the dynamics of quantum many-body systems. These experiments have also posed many new questions. How can we control the dynamics to engineer new states of matter? Given that quantum dynamics is unitary, under which conditions can we expect observables of the system to reach equilibrium values that can be predicted by conventional statistical mechanics? And, how do the observables dynamically approach their statistical equilibrium values? Could the approach to equilibrium be hampered if the system is trapped in long-lived metastable states characterized, for example, by a certain distribution of topological defects? How does the dynamics depend on the way the system is perturbed, such as changing, as a function of time and at a given rate, a parameter across a quantum critical point? What if, conversely, after relaxing to a steady state, the observables cannot be described by the standard equilibrium ensembles of statistical mechanics? How would they depend on the initial conditions in addition to the other properties of the system, such as the existence of conserved quantities? The search for answers to questions like these is fundamental to a new research field that is only beginning to be explored, and to which researchers with different backgrounds, such as nuclear, atomic, and condensed-matter physics, as well as quantum optics, can make, and are making, important contributions. This body of knowledge has an immediate application to experiments in the field of ultracold atomic gases, but can also fundamentally change the way we approach and understand many-body quantum systems. This focus issue of New Journal Physics brings together both experimentalists and theoreticians working on these problems to provide a comprehensive picture of the state of the field. Focus on Dynamics and Thermalization in Isolated Quantum Many-Body Systems Contents Spin squeezing of high-spin, spatially extended quantum fields Jay D Sau, Sabrina R Leslie, Marvin L Cohen and Dan M Stamper-Kurn Thermodynamic entropy of a many-body energy eigenstate J M Deutsch Ground states and dynamics of population-imbalanced Fermi condensates in one dimension Masaki Tezuka and Masahito Ueda Relaxation dynamics in the gapped XXZ spin-1/2 chain Jorn Mossel and Jean-Sébastien Caux Canonical thermalization Peter Reimann Minimally entangled typical thermal state algorithms E M Stoudenmire and Steven R White Manipulation of the dynamics of many-body systems via quantum control methods Julie Dinerman and Lea F Santos Multimode analysis of non-classical correlations in double-well Bose–Einstein condensates Andrew J Ferris and Matthew J Davis Thermalization in a quasi-one-dimensional ultracold bosonic gas I E Mazets and J Schmiedmayer Two simple systems with cold atoms: quantum chaos tests and non-equilibrium dynamics Cavan Stone, Yassine Ait El Aoud, Vladimir A Yurovsky and Maxim Olshanii On the speed of fluctuations around thermodynamic equilibrium Noah Linden, Sandu Popescu, Anthony J Short and Andreas Winter A quantum central limit theorem for non-equilibrium systems: exact local relaxation of correlated states M Cramer and J Eisert Quantum quench dynamics of the sine-Gordon model in some solvable limits A Iucci and M A Cazalilla Nonequilibrium quantum dynamics of atomic dark solitons A D Martin and J Ruostekoski Quantum quenches in the anisotropic spin-1⁄2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium Peter Barmettler, Matthias Punk, Vladimir Gritsev, Eugene Demler and Ehud Altman Crossover from adiabatic to sudden interaction quenches in the Hubbard model: prethermalization and non-equilibrium dynamics Michael Moeckel and Stefan Kehrein Quantum quenches in integrable field theories Davide Fioretto and Giuseppe Mussardo Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point A Bermudez, L Amico and M A Martin-Delgado Thermometry with spin-dependent lattices D McKay and B DeMarco Near-adiabatic parameter changes in correlated systems: influence of the ramp protocol on the excitation energy Martin Eckstein and Marcus Kollar Sudden change of the thermal contact between two quantum systems J Restrepo and S Camalet Reflection of a Lieb–Liniger wave packet from the hard-wall potential D Jukić and H Buljan Probing interaction-induced ferromagnetism in optical superlattices J von Stecher, E Demler, M D Lukin and A M Rey Sudden interaction quench in the quantum sine-Gordon model Javier Sabio and Stefan Kehrein Dynamics of an inhomogeneous quantum phase transition Jacek Dziarmaga and Marek M Rams
Statistical mechanics relies on the maximization of entropy in a system at thermal equilibrium. However, an isolated quantum many-body system initialized in a pure state remains pure during Schrödinger evolution, and in this sense it has static, zero entropy. We experimentally studied the emergence of statistical mechanics in a quantum state and observed the fundamental role of quantum entanglement in facilitating this emergence. Microscopy of an evolving quantum system indicates that the full quantum state remains pure, whereas thermalization occurs on a local scale. We directly measured entanglement entropy, which assumes the role of the thermal entropy in thermalization. The entanglement creates local entropy that validates the use of statistical physics for local observables. Our measurements are consistent with the eigenstate thermalization hypothesis.
Classical statistical mechanics relies on the ergodic hypothesis, which states that a system explores the entire allowed phase space during its time evolution. Pure quantum states are at odds with this concept as they remain in a single quantum state even if the system's parameters are suddenly altered. However, in a generic many-body system, coherent dynamics drive local thermalization of its subsystems. In this case, any local observable appears thermal and can be described by a statistical ensemble even though the full state remains pure. The key to understanding the phenomenon of quantum thermalization lies in the entanglement properties of the system: The presence of entanglement creates local entropy that validates the use of statistical physics.\nIn this thesis, we experimentally study the emergence of statistical mechanics in a quantum state and observe the fundamental role of quantum entanglement in facilitating this emergence. We perform microscopy on an evolving quantum system, and we see thermalization occur on a local scale while we measure that the full quantum state remains pure.\nThe only known robust exception from the paradigm of quantum thermalization is provided by disordered systems. In this case, the particle transport ceases through the system, preventing the formation of a sufficient amount of entanglement required for thermalization. However, if the many-body system is interacting, the state develops non-local quantum correlations that are inaccessible to any local observable. These correlations spread exponentially slowly in time throughout the entire system and are considered a hallmark feature of many-body-localized states.\nIn order to study the interplay between thermalization and localization in our system, we develop novel methods for high fidelity state preparation and readout. We achieved an exquisite isolation of our system from the environment, which allows us to monitor coherent many-body dynamics over multiple decades of time evolution.\nWe experimentally realize such a many-body localized system and observe the formation of non-local quantum correlations, while the particle transport is frozen in the system. Our work experimentally establishes many-body localization as a qualitatively distinct phenomenon from localization in non-interacting, disordered systems.
Quantum Systems
Quantum entanglement occurs when two separate entities become strongly linked in a way that cannot be explained by classical physics; it is a powerful resource in quantum communication protocols and advanced technologies that aim to exploit the enhanced capabilities of quantum systems. To date, entanglement has generally been limited to microscopic quantum units such as pairs or multiples of single ions, atoms, photons, and so on. Kotler et al. and Mercier de Lepinay et al. demonstrate the ability to extend quantum entanglement to massive macroscopic systems (see the Perspective by Lau and Clerk). Entanglement of two mechanical oscillators on such a large length and mass scale is expected to find widespread use in both applications and fundamental physics to probe the boundary between the classical and quantum worlds.
Science , this issue p. [622][1], p. [625][2]; see also p. [570][3]
[1]: /lookup/doi/10.1126/science.abf2998
[2]: /lookup/doi/10.1126/science.abf5389
[3]: /lookup/doi/10.1126/science.abh3419
Among the few lessons that Physics teaches us on a daily basis, one in particular is hard to miss: thermalization processes are ubiquitous. With the same degree of certainty, one can predict an apple to fall onto the ground if its stalk is cut, or a cup of tea to be found cold if left on the table for too long. In this respect, generic classical and quantum mechanical systems seem to behave in the same way. This is also one of the main difficulties in the experimental observation of the bizarre effects predicted from the quantum theory, as several of these are known to disappear at finite temperatures. It has been known for a long time that thermalization is associated with “chaotic” behavior at the microscopic level, but recently systematic efforts, both theoretical and experimental, have allowed us to understand its mechanisms at an unprecedented level of accuracy. Indeed, it has been realized that thermalization generally occurs also in isolated systems, where the absence of interactions with the environment allows for first principle theoretical investigations1. In this case thermalization takes place locally, as the whole system acts as a thermal bath for its own subsystems. Theoretical research has been motivated and paralleled by exciting experimental progress in cold-atom physics, which has provided robust, nearly ideal realizations of several theoretical models2. As an established piece of knowledge, recent research has now confirmed that two outstanding exceptions actually exist in the quantum realm, where thermalization is prevented to occur. These are many-body localized systems3, where disorder plays a crucial role, and integrable ones, which are protected by the existence of higher conservation laws. By their own nature, these systems display exceptional non-equilibrium features, which are not washed out by the onset of thermalization as relaxation occurs. At the core of the present thesis lie the remarkable properties of integrable systems out of equilibrium, with a special attention to physical effects which could be observed in cold-atom realizations. The work collected here is part of a large theoretical effort4 which in the past decade has focused on the study of relatively simple protocols to bring a quantum system out of equilibrium, such as the so-called quantum quench. In these “theoretical laboratories” it has been possible to provide quantitative predictions which helped us to develop an intuition on general questions regarding non-equilibrium and thermalization processes. Furthermore, in some cases these studies have highlighted interesting physical effects which could be directly probed experimentally within cold-atom settings. The contribution of the present thesis is two-fold. On the one hand, we have developed new technical tools for the study of integrable systems out of equilibrium, and for the computation of measurable physical quantities such as correlation functions. The techniques employed are mainly analytical and rooted within the mathematical structures of integrability. On the other hand, we have singled out physically relevant nonequilibrium situations where exotic, non-thermal states of matter emerge after relaxation occurs, and provided quantitative analytical predictions in these cases. A comprehensive discussion of the motivations and results of our work will be presented in Chapter 1, where we provide a complete overview of this thesis and discuss the organization of its content.